A new approach for approximating node deletion problems

We present a new approach for approximating node deletion problems by combining the local ratio and the greedy multicovering algorithms. For a function f : V(G) → ℕ, our approach allows to design a 2 + max _v∈V(G) log f (v) approximation algorithm for the problem of deleting a minimum number of nodes so that the degree of each node v in the remaining graph is at most f(v). This approximation ratio is shown to be asymptotically optimal. The new method is also used to design a 1 + (log2)(k - 1) approximation algorithm for the problem of deleting a minimum number of nodes so that the remaining graph contains no k-bicliques.